Question
Three inlet pipes of equal efficiency can fill a tank in
20 minutes, and two outlet pipes of equal efficiency can empty the tank in 45 minutes. Find the time taken by 1 inlet and 1 outlet pipe together to fill the empty tank.Solution
Time taken by 1 inlet pipe to fill the tank = 20 × 3 = 60 minutes
Time taken by 1 outlet pipe to empty the tank = 45 × 2 = 90 minutes
Let the total capacity of the tank be 180 units (LCM of 60 and 90)
Efficiency of an inlet pipe = (180/60) = 3 units/minute
Efficiency of an outlet pipe = (180/90) = 2 units/minute
So, combined efficiency of 1 inlet and 1 outlet pipe = 3 - 2 = 1 unit/minute
So, required time = (180/1) = 180 minutes = 3 hoursÂ
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